In a second step, we prove in Lemma REF  that the convex hull of any closed and bounded set satisfying the result of Lemma REF  is contained by a submodular polyhedron and contains the corresponding base polyhedron. The proof of this lemma is inspired by the proof of Theorem 1 in [1]}, where the optimality of Edmonds' classical greedy algorithm for linear optimization [2]} is characterized in terms of submodular polyhedra.
